Factors governing the metal coordination number in isolated group IA and IIA metal hydrates

Many of the group IA and IIA metal ions, such as Na+, K+, Mg2+, and Ca2+, play crucial roles in biological functions. Previous theoretical studies generally focus on the number of water molecules bound to a particular ( as opposed to all) alkali or alkaline earth cations and could not establish a single preferred CN for the heavier alkali and alkaline earth ion - water complexes. Crystal structures of hydrated Na+, K+, and Rb+ also cannot establish the preferred number of inner-shell water molecules bound to these cations. Consequently, it is unclear if the gas-phase CNs of group IA metal hydrates increase with increasing ion size, as observed for the group IIA series from the Cambridge Structural Database, and if the same factors govern the gas-phase CNs of both group IA and IIA ion - water complexes. Thus, in this work, we determine the number of water molecules directly bound to the series of alkali (Li+, Na+, K+, and Rb+) and alkaline earth (Be2+, Mg2+, Ca2+, Sr2+, and Ba2+) metal ions in the gas phase by computing the free energy for forming an isolated metal - aqua complex as a function of the number of water molecules at 298 K. The preferred gas-phase CNs of group IA hydrates appear insensitive to the ion size; they are all 4, except for Rb+, where a CN of 6 seems as likely. In contrast, the preferred gas-phase CNs of the group IIA dications increase with increasing ion size; they are 4 for Be2+, 6 for Mg2+ and Ca2+, and 7 for Sr2+ and Ba2+. An entropic penalty disfavors a gas-phase CN greater than 4 for group IA hydrates, but it does not dictate the gas-phase CNs of group IIA hydrates. Instead, interactions between the metal ion and first-shell water molecules and between first-shell and second-shell water molecules govern the preferred gas-phase CNs of the group IIA metal hydrates.